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function [a,b,e,ret]=takeStep(i, j, a1, C, e1, Y, X, eps, b1, N, dim)
a = a1;
e = e1;
b = b1;
ret = 1;
if i == j
ret =0;
end
if( ret ~= 0)
%variable initialization%
a_old = a;
if a_old(i,1) > 0 && a_old(i,1) < C
Ei = e(i,1);
else
Ei = cal_learned_func(i, a, b, N, Y, X, dim) - Y(i,1);
end
if a_old(j,1) > 0 && a_old(j,1) < C
Ej = e(j,1);
else
Ej = cal_learned_func(j, a, b, N, Y, X, dim) - Y(j,1);
end
s = Y(i,1) * Y(j,1);
%Compute L, H%
if Y(i,1) == Y(j,1)
gamma = a_old(i,1) + a_old(j,1);
if gamma > C
L = gamma-C;
H = C;
else
L = 0;
H = gamma;
end
else
gamma = a_old(i,1) - a_old(j,1);
if gamma > 0
L = 0;
H = C - gamma;
else
L = -gamma;
H = C;
end
end
if L == H
ret=0;
end
end
if(ret ~=0)
% %Compute eta
k11 = polynomial(3,X(i,:), X(i,:), dim);
k12 = polynomial(3,X(i,:), X(j,:), dim);
k22 = polynomial(3,X(j,:), X(j,:), dim);
eta = 2 * k12 - k11 - k22;
if eta < 0
a(j,1) = a_old(j,1) + Y(j,1) * (Ej - Ei) / eta;
if a(j,1) < L
a(j,1) = L;
elseif a(j,1) > H
a(j,1) = H;
end
else
%Compute Lobj, Hobj: objective function at a2=L, a2=H 22di
c1 = eta/2;
c2 = Y(j,1) * (Ei-Ej)- eta * a_old(j,1);
Lobj = c1 * L * L + c2 * L;
Hobj = c1 * H * H + c2 * H;
if (Lobj > Hobj+eps)
a(j,1) = L;
elseif (Lobj < Hobj-eps)
a(j,1) = H;
else
a(j,1) = a_old(j,1);
end
end
end
if( ret~= 0)
if abs(a(j,1)-a_old(j,1)) < eps*(a(j,1)+a_old(j,1)+eps)
ret=0;
else
a(i,1) = a_old(i,1) - s * (a(j,1) - a_old(j,1));
if a(i,1) < 0
a(j,1) = a(j,1) + s * a(i,1);
a(i,1) = 0;
elseif a(i,1) > C
t = a(i,1)-C;
a(j,1) = a(j,1) + s * t;
a(i,1) = C;
end
%Update threshold to reect change in Lagrange multipliers
if a(i,1) > 0 && a(i,1) < C
bnew = b + Ei + Y(i,1) * (a(i,1) - a_old(i,1)) * k11 + Y(j,1) * (a(j,1) - a_old(j,1)) * k12;
else
if a(j,1) > 0 && a(j,1) < C
bnew = b + Ej + Y(i,1) * (a(i,1) - a_old(i,1)) * k12 + Y(j,1) * (a(j,1) - a_old(j,1)) * k22;
else
b1 = b + Ei + Y(i,1) * (a(i,1) - a_old(i,1)) * k11 + Y(j,1) * (a(j,1) - a_old(j,1)) * k12;
b2 = b + Ej + Y(i,1) * (a(i,1) - a_old(i,1)) * k12 + Y(j,1) * (a(j,1) - a_old(j,1)) * k22;
bnew = (b1 + b2) / 2;
end
end
delta_b = bnew - b;
b = bnew;
%Update error cache using new Lagrange multipliers 24ai
t1 = Y(i,1) * (a(i,1)-a_old(i,1));
t2 = Y(j,1) * (a(j,1)-a_old(j,1));
for k=1:N
if 0 < a_old(i,1) && a_old(i,1) < C
e(k,1) = e(k,1)+t1 * polynomial(3,X(i,:),X(k,:),dim) + t2 * polynomial(3,X(j,:),X(k,:),dim) - delta_b;
e(i,1) = 0;
e(j,1) = 0;
end
end
ret = 1;
end
end
end
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